BAB IVPENGUMPULAN DAN PENGOLAHAN DATA

4.1 PENGUMPULAN DATA

4.1.1 Tabel Data Kerusakan Mesin

No Nama Mesin1 Press 392 Cutting 893 Bubut 564 Milling 345 Bor 59

Σ 277

4.1.2. Data Kerusakan Komponen Pada Mesin

No1 Quill 202 Spindle 93 Work table 344 Feed control 295 Speed control 166 Conector moto 267 Power head 468 Table adjusti 189 Base 30

Jumlah 228

Data Kerusakan

Nama komponen

Data Kerusakan

4.1.3. Tabel Data Waktu Reparasi Mesin Cutting komponen Power Head(Kerusakan-Kerusakan Besar)

No Jam Kerusakan

1 6-Jan-12 15:02 - 15:33 0.517 0:312 15-Jan-12 15:16 - 15:42 0.433 0:263 26-Jan-12 17:55 - 20:52 2.950 2:574 27-Jan-12 8:40 - 11:45 3.083 3:055 29-Jan-12 18:46 - 20:52 2.100 2:066 31-Jan-12 9:23 - 10:38 1.250 1:157 14-Feb-12 6:16 - 9:45 3.483 3:298 22-Feb-12 0:15 - 5:30 5.250 5:159 23-Feb-12 4:10 - 6:05 6.667 6:4010 25-Feb-12 4:25 - 5:05 0.667 0:4011 1-Mar-12 9:28 - 14:00 4.533 4:3212 8-Mar-12 19:12 - 22:55 3.717 3:4313 11-Mar-12 1:11 - 1:20 0.150 0:0914 14-Mar-12 1:25 - 3:57 2.533 2:3215 21-Mar-12 11:43 - 12:43 1.000 1:0016 2-Apr-12 15:41 - 16:55 1.233 1:1417 11-Apr-12 8:40 - 14:40 6.000 6:0018 16-Apr-12 14:50 - 16:13 4.067 4:0419 29-Apr-12 0:48 - 1:48 1.000 1:0020 22-May-12 12:01 - 12:10 0.150 0:0921 25-May-12 8:34 - 11:54 3.333 3:2022 27-May-12 9:40 - 11:46 7.000 7:0023 30-May-12 8:16 - 14:20 6.067 6:0424 3-Jun-12 14:49 - 14:58 0.150 0:0925 9-Jun-12 20:59 - 22:55 1.933 1:5626 26-Jun-12 8:16 - 14:16 6.000 6:0027 11-Jul-12 23:05 - 23:20 0.250 0:1528 16-Jul-12 13:00 - 16:18 3.300 3:1829 23-Jul-12 19:10 - 21:46 2.600 2:3630 24-Jul-12 10:11 - 11:58 1.783 1:4731 28-Jul-12 12:20 - 13:10 0.833 0:5032 16-Aug-12 18:05 - 19:46 1.683 1:4133 19-Aug-12 4:32 - 6:25 1.883 1:5334 26-Aug-12 6:32 - 9:20 2.800 2:4835 12-Sep-12 12:22 - 18:53 6.517 6:3136 20-Sep-12 15:55 - 18:45 2.833 2:5037 26-Sep-12 15:45 - 15:58 0.217 0:1338 29-Sep-12 19:08 - 21:00 1.867 1:5239 1-Oct-12 19:17 - 21:02 1.750 1:4540 23-Oct-12 2:10 - 6:15 4.083 4:0541 26-Oct-12 3:48 - 5:50 2.033 2:0242 8-Nov-12 14:55 - 20:52 5.950 5:5743 9-Nov-12 10:59 - 13:40 2.683 2:4144 16-Nov-12 18:36 - 19:11 0.583 0:3545 22-Nov-12 9:28 - 10:36 1.133 1:08

Tanggal Kerusakan

Waktu Reparasi (jam)

46 6-Dec-12 15:10 - 15:24 0.233 0:14

4.2. PENGOLAHAN DATA

4.2.1. Diagram Pareto4.2.1.1. Tabel Diagram Pareto Untuk Kerusakan pada Mesin

Tabel Diagram Pareto

No Nama Mesin1 Cutting 89 32.13% 89 32.13%2 Bor 59 21.30% 148 53.43%3 Bubut 56 20.22% 204 73.65%4 Press 39 14.08% 243 87.73%5 Milling 34 12.27% 277 100%

Jumlah 277 100.00%

frekuensi Kerusakan

Persentase kerusakan

Frekuensi Kumulatif

Persentase kumulatif

Cutting Bor Bubut Press Milling050100150200250

0.00%

20.00%

40.00%

60.00%

80.00%

100.00%Diagram Pareto Kerusakan Mesin

Frekuensi Kerusakan Presentasi Kumulatif

Frek

uens

i Ke

rusa

kan

Mesin

Pres

enta

se K

umul

atif

4.2.1.2. Diagram Pareto Untuk Data Kerusakan Komponen pada Mesin CuttingTabel pengurutan data kerusakan

No1 Power head 462 Work table 343 Base 304 Feed Control 295 Conector moto 266 Quill 207 Table adjusti 188 Speed Control 169 Spindle 9

Jumlah 228

Tabel Diagram Pareto

No1 Power head 46 20.18% 46 20.18%2 Work table 34 14.91% 80 35.09%3 Base 30 13.16% 110 48.25%4 Feed Control 29 12.72% 139 60.96%5 Conector moto 26 11.40% 165 72.37%6 Quill 20 8.77% 185 81.14%7 Table adjusti 18 7.89% 203 89.04%8 Speed Control 16 7.02% 219 96.05%9 Spindle 9 3.95% 228 100%

Jumlah 228 100.00%

Nama komponen

Data Kerusakan

Nama Komponen

frekuensi Kerusakan

Persentase kerusakan

Frekuensi Kumulatif

Persentase kumulatif

050

100150200

0.00%20.00%40.00%60.00%80.00%100.00%

Diagram Pareto Kerusakan Komponen Mesin Cutting

Frekuensi Kerusakan Presentase KumulatifKomponen

Frek

uens

i Ke

rusa

kan

Pres

enta

se K

umul

atif

4.2.2 Tabel Data Waktu Reparasi Mesin Cutting Komponen Power Head(Kerusakan-Kerusakan Besar)

No Jam Kerusakan1 6-Jan-12 15:02 - 17:33 2.5172 15-Jan-12 15:16 - 15:42 0.4333 26-Jan-12 17:55 - 20:52 2.9504 27-Jan-12 8:40 - 11:45 3.0835 29-Jan-12 18:46 - 20:52 2.1006 31-Jan-12 9:23 - 10:38 1.2507 14-Feb-12 6:16 - 9:45 3.4838 22-Feb-12 0:15 - 5:30 5.2509 23-Feb-12 4:10 - 6:05 1.91710 25-Feb-12 4:25 - 5:05 0.66711 1-Mar-12 9:28 - 14:00 4.53312 8-Mar-12 19:12 - 22:55 3.71713 11-Mar-12 1:11 - 1:20 0.15014 14-Mar-12 1:25 - 3:57 2.53315 21-Mar-12 11:43 - 12:43 1.00016 2-Apr-12 15:41 - 16:55 1.23317 11-Apr-12 8:40 - 14:40 6.00018 16-Apr-12 14:50 - 16:13 1.38319 29-Apr-12 0:48 - 1:48 1.00020 22-May-12 12:01 - 12:10 0.15021 25-May-12 8:34 - 11:54 3.33322 27-May-12 9:40 - 11:46 2.10023 30-May-12 8:16 - 14:20 6.06724 3-Jun-12 14:49 - 14:58 0.15025 9-Jun-12 20:59 - 22:55 1.93326 26-Jun-12 8:16 - 14:16 6.00027 11-Jul-12 23:05 - 23:20 0.25028 16-Jul-12 13:00 - 16:18 3.30029 23-Jul-12 19:10 - 21:46 2.60030 24-Jul-12 10:11 - 11:58 1.78331 28-Jul-12 12:20 - 13:10 0.83332 16-Aug-12 18:05 - 19:46 1.68333 19-Aug-12 4:32 - 6:25 1.88334 26-Aug-12 6:32 - 9:20 2.80035 12-Sep-12 12:22 - 18:53 6.51736 20-Sep-12 15:55 - 18:45 2.83337 26-Sep-12 15:45 - 15:58 0.21738 29-Sep-12 19:08 - 21:00 1.86739 1-Oct-12 19:17 - 21:02 1.75040 23-Oct-12 2:10 - 6:15 4.08341 26-Oct-12 3:48 - 5:50 2.03342 8-Nov-12 14:55 - 20:52 5.95043 9-Nov-12 10:59 - 13:40 2.68344 16-Nov-12 18:36 - 19:11 0.583

Tanggal Kerusakan

Waktu Reparasi (Jam)

45 22-Nov-12 9:28 - 10:36 1.13346 6-Dec-12 15:10 - 15:24 0.233

No Jam Kerusakan1 11-Mar-12 1:11 - 1:20 0.15020 22-May-12 12:01 - 12:10 0.15024 3-Jun-12 14:49 - 14:58 0.15037 26-Sep-12 15:45 - 15:58 0.21746 6-Dec-12 15:10 - 15:24 0.23327 11-Jul-12 23:05 - 23:20 0.2502 15-Jan-12 15:16 - 15:42 0.43344 16-Nov-12 18:36 - 19:11 0.58310 25-Feb-12 4:25 - 5:05 0.66731 28-Jul-12 12:20 - 13:10 0.83315 21-Mar-12 11:43 - 12:43 1.00019 29-Apr-12 0:48 - 1:48 1.00045 22-Nov-12 9:28 - 10:36 1.13316 2-Apr-12 15:41 - 16:55 1.2336 31-Jan-12 9:23 - 10:38 1.25018 16-Apr-12 14:50 - 16:13 1.38332 16-Aug-12 18:05 - 19:46 1.68339 1-Oct-12 19:17 - 21:02 1.75030 24-Jul-12 10:11 - 11:58 1.78338 29-Sep-12 19:08 - 21:00 1.86733 19-Aug-12 4:32 - 6:25 1.8839 23-Feb-12 4:10 - 6:05 1.91725 9-Jun-12 20:59 - 22:55 1.93341 26-Oct-12 3:48 - 5:50 2.0335 29-Jan-12 18:46 - 20:52 2.10022 27-May-12 9:40 - 11:46 2.1001 6-Jan-12 15:02 - 17:33 2.51714 14-Mar-12 1:25 - 3:57 2.53329 23-Jul-12 19:10 - 21:46 2.60043 9-Nov-12 10:59 - 13:40 2.68334 26-Aug-12 6:32 - 9:20 2.80036 20-Sep-12 15:55 - 18:45 2.8333 26-Jan-12 17:55 - 20:52 2.9504 27-Jan-12 8:40 - 11:45 3.08328 16-Jul-12 13:00 - 16:18 3.30021 25-May-12 8:34 - 11:54 3.3337 14-Feb-12 6:16 - 9:45 3.48312 8-Mar-12 19:12 - 22:55 3.71740 23-Oct-12 2:10 - 6:15 4.08311 1-Mar-12 9:28 - 14:00 4.5338 22-Feb-12 0:15 - 5:30 5.25042 8-Nov-12 14:55 - 20:52 5.95017 11-Apr-12 8:40 - 14:40 6.00026 26-Jun-12 8:16 - 14:16 6.00023 30-May-12 8:16 - 14:20 6.06735 12-Sep-12 12:22 - 18:53 6.517

Berikut ini adalah tabel waktu reparasi komponen mesin yang telah di-

Tanggal Kerusakan

Urutan waktu reparasi

4.2.3 Perhitungan Distribusi Weibull untuk Waktu Reparasi Komponen Power Head

No XiZi

(i)1 0.150 -1.897 -4.522 1.110 0.000 0.0002 0.150 -1.897 -3.412 0.522 0.000 0.0003 0.150 -1.897 -2.890 0.348 0.368 1.0574 0.217 -1.529 -2.542 0.263 0.074 0.2825 0.233 -1.455 -2.279 0.213 0.069 0.3256 0.250 -1.386 -2.067 0.179 0.550 3.0707 0.433 -0.836 -1.887 0.155 0.297 1.9128 0.583 -0.539 -1.732 0.138 0.134 0.9699 0.667 -0.405 -1.594 0.124 0.223 1.79710 0.833 -0.182 -1.470 0.113 0.182 1.60911 1.000 0.000 -1.357 0.105 0.000 0.00012 1.000 0.000 -1.252 0.097 0.125 1.28713 1.133 0.125 -1.155 0.091 0.085 0.92714 1.233 0.210 -1.064 0.086 0.013 0.15615 1.250 0.223 -0.978 0.082 0.101 1.23816 1.383 0.324 -0.896 0.078 0.197 2.52317 1.683 0.521 -0.818 0.075 0.039 0.52018 1.750 0.560 -0.744 0.072 0.019 0.26319 1.783 0.578 -0.672 0.069 0.046 0.65820 1.867 0.624 -0.602 0.067 0.009 0.13221 1.883 0.633 -0.535 0.065 0.018 0.27122 1.917 0.651 -0.470 0.064 0.008 0.13323 1.933 0.659 -0.406 0.063 0.050 0.80624 2.033 0.710 -0.343 0.061 0.032 0.52525 2.100 0.742 -0.282 0.061 0.000 0.00026 2.100 0.742 -0.221 0.060 0.181 3.02927 2.517 0.923 -0.161 0.059 0.006 0.10928 2.533 0.930 -0.102 0.059 0.026 0.44129 2.600 0.956 -0.043 0.059 0.032 0.53730 2.683 0.987 0.016 0.059 0.043 0.72331 2.800 1.030 0.074 0.059 0.012 0.20032 2.833 1.041 0.133 0.060 0.040 0.67733 2.950 1.082 0.193 0.060 0.044 0.73234 3.083 1.126 0.254 0.061 0.068 1.10535 3.300 1.194 0.315 0.063 0.010 0.16036 3.333 1.204 0.378 0.065 0.044 0.68037 3.483 1.248 0.443 0.067 0.065 0.96538 3.717 1.313 0.510 0.070 0.094 1.33739 4.083 1.407 0.580 0.074 0.105 1.40340 4.533 1.511 0.655 0.080 0.147 1.83441 5.250 1.658 0.735 0.088 0.125 1.42742 5.950 1.783 0.822 0.099 0.008 0.08543 6.000 1.792 0.921 0.116 0.000 0.00044 6.000 1.792 1.038 0.149 0.011 0.07445 6.067 1.803 1.186 0.230 0.072 0.31146 6.517 1.874 1.416

Jumlah 5.938 3.771 36.289Keterangan :Rank umur (ti) = waktu reparasi yang diurutkan kecil ke besarXi = ln(ti)

Rank Umur (ti) Mi ln(ti + 1) - ln(ti)(ln(ti + 1) - ln(ti)) / Mi(ln ti)

iii ZZM 1

25.05.01lnln

niZ i

4.2.4. Pengujian kecocokan Distribusi / Pengujian Mann's Test

Ho : Data berdistribusi WeibullHa : Data tidak berdistribusi Weibull

r = Banyaknya data (n)= 46

=462

= 23

=( 46 - 1 )

2

= 22.5

daerah penerimaan

=23 x 36.289

22.5 x 36.3289 daerah penolakan

= 1.022

Numerator Denominator = 2 x 22.5 = 2 x 23 = 45 = 46

F(0.05,N,D) =1.636 FINV(0.05, Numerator, Denumerator)

Jika M < F crit maka terima Ho dan tolak HaJika M > F crit maka tolak Ho dan terima HaKesimpulan :Karena M < F yaitu 1.022 < 1.636 , terima Ho dan tolak Ha.Dari kesimpulan diatas, maka dapat diketahui bahwa data waktu reparasi dari komponen mesin tersebut adalah berdistribusi Weibull. Maka dari itu, dapat dilakukan perhitungan plot Weibull.

2k2 2k1

21rk

21

2

rk

1

1

1

12

1

1

11

lnln

lnln

k

i i

ii

r

ki i

ii

Mttk

Mttk

M

5%

1.022

1.636

=

23 ∑i=24

45 lnti+1−lntiMi

22.5∑i=1

23 lnti+1−lntiMi

4.2.5 Tabel Perhitungan Plot Weibull Waktu Reparasi Komponen Power Head

i ti Xi = ln ti F ( ti )1 / {1 - F (ti)} ln ( E ) Yi = ln ( F )A B C D E F G1 0.150 -1.897 0.015 1.015 0.015 -4.1862 0.150 -1.897 0.037 1.038 0.037 -3.2883 0.150 -1.897 0.058 1.062 0.060 -2.8144 0.217 -1.529 0.080 1.087 0.083 -2.4885 0.233 -1.455 0.101 1.113 0.107 -2.2376 0.250 -1.386 0.123 1.140 0.131 -2.0327 0.433 -0.836 0.144 1.169 0.156 -1.8588 0.583 -0.539 0.166 1.199 0.181 -1.7079 0.667 -0.405 0.188 1.231 0.208 -1.57210 0.833 -0.182 0.209 1.264 0.235 -1.45011 1.000 0.000 0.231 1.300 0.262 -1.33912 1.000 0.000 0.252 1.337 0.291 -1.23613 1.133 0.125 0.274 1.377 0.320 -1.14014 1.233 0.210 0.295 1.419 0.350 -1.05015 1.250 0.223 0.317 1.464 0.381 -0.96516 1.383 0.324 0.338 1.511 0.413 -0.88417 1.683 0.521 0.360 1.562 0.446 -0.80718 1.750 0.560 0.381 1.617 0.480 -0.73319 1.783 0.578 0.403 1.675 0.516 -0.66220 1.867 0.624 0.425 1.738 0.553 -0.59321 1.883 0.633 0.446 1.805 0.591 -0.52622 1.917 0.651 0.468 1.879 0.630 -0.46123 1.933 0.659 0.489 1.958 0.672 -0.39824 2.033 0.710 0.511 2.044 0.715 -0.33625 2.100 0.742 0.532 2.138 0.760 -0.27426 2.100 0.742 0.554 2.242 0.807 -0.21427 2.517 0.923 0.575 2.355 0.857 -0.15528 2.533 0.930 0.597 2.481 0.909 -0.09629 2.600 0.956 0.619 2.621 0.964 -0.03730 2.683 0.987 0.640 2.778 1.022 0.02231 2.800 1.030 0.662 2.955 1.084 0.08032 2.833 1.041 0.683 3.156 1.149 0.13933 2.950 1.082 0.705 3.387 1.220 0.19934 3.083 1.126 0.726 3.654 1.296 0.25935 3.300 1.194 0.748 3.966 1.378 0.32036 3.333 1.204 0.769 4.336 1.467 0.38337 3.483 1.248 0.791 4.784 1.565 0.44838 3.717 1.313 0.813 5.333 1.674 0.51539 4.083 1.407 0.834 6.026 1.796 0.58640 4.533 1.511 0.856 6.925 1.935 0.66041 5.250 1.658 0.877 8.140 2.097 0.74042 5.950 1.783 0.899 9.872 2.290 0.82843 6.000 1.792 0.920 12.541 2.529 0.92844 6.000 1.792 0.942 17.185 2.844 1.04545 6.067 1.803 0.963 27.294 3.307 1.19646 6.517 1.874 0.985 66.286 4.194 1.434

Grafik 4.1 Plot Weibull Waktu Reparasi Mesin Cutting komponen Power Head

-3 -2 -1 0 1 2 3

-5-4-3-2-1012

Plot Weibull Waktu Reparasi (Xi vs Yi)

Xi

Yi

4,03,0

nitiF

4.2.6 Tabel Parameter Weibull dari Waktu Reparasi komponen Power Head

i Xi Yi XiYi1 -1.897 -4.186 7.942 3.5992 -1.897 -3.288 6.238 3.5993 -1.897 -2.814 5.339 3.5994 -1.529 -2.488 3.805 2.3395 -1.455 -2.237 3.255 2.1186 -1.386 -2.032 2.817 1.9227 -0.836 -1.858 1.554 0.6998 -0.539 -1.707 0.920 0.2919 -0.405 -1.572 0.637 0.16410 -0.182 -1.450 0.264 0.03311 0.000 -1.339 0.000 0.00012 0.000 -1.236 0.000 0.00013 0.125 -1.140 -0.143 0.01614 0.210 -1.050 -0.220 0.04415 0.223 -0.965 -0.215 0.05016 0.324 -0.884 -0.287 0.10517 0.521 -0.807 -0.420 0.27118 0.560 -0.733 -0.410 0.31319 0.578 -0.662 -0.383 0.33520 0.624 -0.593 -0.370 0.39021 0.633 -0.526 -0.333 0.40122 0.651 -0.461 -0.300 0.42323 0.659 -0.398 -0.262 0.43524 0.710 -0.336 -0.238 0.50425 0.742 -0.274 -0.204 0.55026 0.742 -0.214 -0.159 0.55027 0.923 -0.155 -0.143 0.85228 0.930 -0.096 -0.089 0.86429 0.956 -0.037 -0.035 0.91330 0.987 0.022 0.021 0.97431 1.030 0.080 0.083 1.06032 1.041 0.139 0.145 1.08533 1.082 0.199 0.215 1.17034 1.126 0.259 0.292 1.26835 1.194 0.320 0.383 1.42536 1.204 0.383 0.461 1.45037 1.248 0.448 0.559 1.55738 1.313 0.515 0.676 1.72439 1.407 0.586 0.824 1.97940 1.511 0.660 0.998 2.28541 1.658 0.740 1.228 2.75042 1.783 0.828 1.477 3.18043 1.792 0.928 1.662 3.21044 1.792 1.045 1.873 3.21045 1.803 1.196 2.156 3.25046 1.874 1.434 2.687 3.513

Jumlah 21.930 -25.755 44.300 60.471

= 46(44.300) - (21.930)(-25.755) = exp

= 1.131 = 2.642

MTTR = θ

== 2.642

= -1.099= 4.978 jam

b

Xi2

46(60.471) - (21.930)2

β =

22

ii

iiii

XXnYXYXn

b

nX

bnY

a ii

θ=exp(−ab )

(−25.755)46

−1.131 (21.930)46

[−(1.099 )¿1.131 ¿

¿¿]

[1+1β ][1+

11.131 ]

= 1.131

4.2.7 Perhitungan fungsi - fungsi distribusi Weibull untuk komponen Power Head

Fungsi distribusi kumulatif waktu reparasi : Fungsi keandalan waktu Reparasi :

Fungsi kepadatan kemungkinan waktu reparasi : Fungsi laju kerusakan :

4.2.7.1 Tabel Hasil Perhitungan Fungsi Distribusi Kumulatif, Fungsi Kepadatan Kemungkinan Fungsi Keandalan, dan Fungsi Laju Kerusakan Waktu Reparasi Power Head

R ( t ) F ( t ) f ( t ) h ( t )0.150 0.962 0.038 0.283 0.2940.150 0.962 0.038 0.283 0.2940.150 0.962 0.038 0.283 0.2940.217 0.943 0.057 0.291 0.3080.233 0.938 0.062 0.292 0.3110.250 0.933 0.067 0.293 0.3140.433 0.879 0.121 0.297 0.3380.583 0.834 0.166 0.293 0.3510.667 0.810 0.190 0.289 0.3570.833 0.763 0.237 0.281 0.3681.000 0.717 0.283 0.270 0.3771.000 0.717 0.283 0.270 0.3771.133 0.681 0.319 0.261 0.3831.233 0.656 0.344 0.254 0.3871.250 0.651 0.349 0.253 0.3881.383 0.618 0.382 0.243 0.3931.683 0.549 0.451 0.221 0.4041.750 0.534 0.466 0.217 0.4061.783 0.527 0.473 0.214 0.4071.867 0.509 0.491 0.208 0.4091.883 0.506 0.494 0.207 0.4091.917 0.499 0.501 0.205 0.4101.933 0.495 0.505 0.204 0.4112.033 0.475 0.525 0.197 0.4142.100 0.462 0.538 0.192 0.4152.100 0.462 0.538 0.192 0.4152.517 0.388 0.612 0.165 0.4252.533 0.385 0.615 0.164 0.4262.600 0.375 0.625 0.160 0.4272.683 0.361 0.639 0.155 0.4292.800 0.344 0.656 0.148 0.4312.833 0.339 0.661 0.146 0.4322.950 0.322 0.678 0.140 0.4343.083 0.304 0.696 0.133 0.4373.300 0.276 0.724 0.122 0.4413.333 0.272 0.728 0.120 0.4413.483 0.255 0.745 0.113 0.4443.717 0.230 0.770 0.103 0.4484.083 0.195 0.805 0.088 0.4534.533 0.159 0.841 0.073 0.4605.250 0.114 0.886 0.053 0.4685.950 0.082 0.918 0.039 0.4766.000 0.080 0.920 0.038 0.4776.000 0.080 0.920 0.038 0.4776.067 0.077 0.923 0.037 0.477

ti

f (t)=βθ (tθ)

β−1exp [−(tθ)

β ]

F (t )=1−exp[−(tθ)β ]

=1−exp[−( t4.978 )

1.131]R (t)=exp[−(tθ )

β]

h (t )=βθ (tθ )

β−1

=exp[−( t4.978 )

1.131 ]

=1.1314.978 ( t

4.978 )1.131−1

exp[( t4.978 )

1.131 ] =1.1314.978 ( t

4.978 )1.131−1

6.517 0.062 0.938 0.030 0.482

Berdasarkan perhitungan pada tabel diatas, maka dapat ditentukan kurva dari beberapa fungsi yang dapat dilihat pada gambar berikut :

Gmabar 5.2 Kurva fungsi keandalan waktu reparasi

Gmabar 5.3 Kurva fungsi distribusi kumulatif waktu reparasi

Gmabar 5.4 Kurva fungsi kepadatan kemungkinan waktu reparasi

Gmabar 5.5 Kurva fungsi laju kerusakan

0 1 2 3 4 5 6 70.000.200.400.600.801.00

Kurva Fungsi Distribusi Kumulatif Waktu Reparasi

t (jam)

F(t)

0 1 2 3 4 5 6 70.000

0.100

0.200

0.300

0.400Kurva Fungsi Kepadatan Kemungkinan Waktu Reparasi

t (jam)

f(t)

0 1 2 3 4 5 6 70.000

0.500

1.000

1.500Kurva Fungsi Keandalan Waktu Reparasi

t (jam)

R(t)

0 1 2 3 4 5 6 70.000

0.200

0.400

0.600Kurva Fungsi Laju Kerusakan

t (jam)

h(t)

4.2.8 Tabel Data Waktu Reparasi Mesin Cutting Komponen Power Head(Kerusakan-Kerusakan Besar)

Jika dilihat pada tabel waktu reparasi pada tabel 4.2.2, masih terdapat nilai waktu reparasi yang lebih kecil dari 1.00Oleh karena itu, perlu dilakukan iterasi. Adapun hasil iterasi tersebut adalah sebagai berikut.

No Jam Kerusakan1 6-Jan-12 15:02 - 17:33 2.517 ###3 26-Jan-12 17:55 - 20:52 2.950 ###4 27-Jan-12 8:40 - 11:45 3.083 ###5 29-Jan-12 18:46 - 20:52 2.100 ###6 31-Jan-12 9:23 - 10:38 1.250 ###7 14-Feb-12 6:16 - 9:45 3.483 ###8 22-Feb-12 0:15 - 5:30 5.2509 23-Feb-12 4:10 - 6:05 1.917 ###11 1-Mar-12 9:28 - 14:00 4.533 ###12 8-Mar-12 19:12 - 22:55 3.717 ###14 14-Mar-12 1:25 - 3:57 2.533 ###15 21-Mar-12 11:43 - 12:43 1.000 ###16 2-Apr-12 15:41 - 16:55 1.233 ###17 11-Apr-12 8:40 - 14:40 6.000 ###18 16-Apr-12 14:50 - 16:13 1.383 ###19 29-Apr-12 0:48 - 1:48 1.000 ###21 25-May-12 8:34 - 11:54 3.333 ###22 27-May-12 9:40 - 11:46 2.100 ###23 30-May-12 8:16 - 14:20 6.06725 9-Jun-12 20:59 - 22:55 1.933 ###26 26-Jun-12 8:16 - 14:16 6.000 ###28 16-Jul-12 13:00 - 16:18 3.300 ###29 23-Jul-12 19:10 - 21:46 2.600 ###30 24-Jul-12 10:11 - 11:58 1.783 ###32 16-Aug-12 18:05 - 19:46 1.68333 19-Aug-12 4:32 - 6:25 1.88334 26-Aug-12 6:32 - 9:20 2.80035 12-Sep-12 12:22 - 18:53 6.51736 20-Sep-12 15:55 - 18:45 2.83338 29-Sep-12 19:08 - 21:00 1.86739 1-Oct-12 19:17 - 21:02 1.75040 23-Oct-12 2:10 - 6:15 4.08341 26-Oct-12 3:48 - 5:50 2.03342 8-Nov-12 14:55 - 20:52 5.95043 9-Nov-12 10:59 - 13:40 2.68345 22-Nov-12 9:28 - 10:36 1.133

Tanggal Kerusakan

Waktu Reparasi (Jam)

setelah di array

No Jam Kerusakan

15 21-Mar-12 11:43 - 12:43 1.00019 29-Apr-12 0:48 - 1:48 1.00045 22-Nov-12 9:28 - 10:36 1.13316 2-Apr-12 15:41 - 16:55 1.2336 31-Jan-12 9:23 - 10:38 1.25018 16-Apr-12 14:50 - 16:13 1.38332 16-Aug-12 18:05 - 19:46 1.68339 1-Oct-12 19:17 - 21:02 1.75030 24-Jul-12 10:11 - 11:58 1.78338 29-Sep-12 19:08 - 21:00 1.86733 19-Aug-12 4:32 - 6:25 1.8839 23-Feb-12 4:10 - 6:05 1.91725 9-Jun-12 20:59 - 22:55 1.93341 26-Oct-12 3:48 - 5:50 2.0335 29-Jan-12 18:46 - 20:52 2.10022 27-May-12 9:40 - 11:46 2.1001 6-Jan-12 15:02 - 17:33 2.51714 14-Mar-12 1:25 - 3:57 2.53329 23-Jul-12 19:10 - 21:46 2.60043 9-Nov-12 10:59 - 13:40 2.68334 26-Aug-12 6:32 - 9:20 2.80036 20-Sep-12 15:55 - 18:45 2.8333 26-Jan-12 17:55 - 20:52 2.9504 27-Jan-12 8:40 - 11:45 3.08328 16-Jul-12 13:00 - 16:18 3.30021 25-May-12 8:34 - 11:54 3.3337 14-Feb-12 6:16 - 9:45 3.48312 8-Mar-12 19:12 - 22:55 3.71740 23-Oct-12 2:10 - 6:15 4.08311 1-Mar-12 9:28 - 14:00 4.5338 22-Feb-12 0:15 - 5:30 5.25042 8-Nov-12 14:55 - 20:52 5.95017 11-Apr-12 8:40 - 14:40 6.00026 26-Jun-12 8:16 - 14:16 6.00023 30-May-12 8:16 - 14:20 6.06735 12-Sep-12 12:22 - 18:53 6.517

Tanggal Kerusakan

Waktu Reparasi (Jam)

4.2.8.1. Perhitungan Distribusi Weibull untuk Waktu Reparasi Komponen Power Head

No Xi Zi(i)1 1.000 0.000 -3.569 0.708 0.000 0.0002 1.000 0.000 -2.862 0.420 0.125 0.2983 1.133 0.125 -2.442 0.303 0.084 0.2784 1.233 0.209 -2.139 0.239 0.014 0.0575 1.250 0.223 -1.900 0.198 0.101 0.5106 1.383 0.324 -1.702 0.171 0.196 1.1517 1.683 0.521 -1.531 0.150 0.039 0.2608 1.750 0.560 -1.381 0.135 0.019 0.1389 1.783 0.578 -1.246 0.123 0.046 0.37210 1.867 0.624 -1.123 0.114 0.009 0.07711 1.883 0.633 -1.009 0.106 0.018 0.16912 1.917 0.651 -0.903 0.100 0.008 0.08513 1.933 0.659 -0.803 0.095 0.050 0.53314 2.033 0.710 -0.708 0.090 0.032 0.35715 2.100 0.742 -0.618 0.087 0.000 0.00016 2.100 0.742 -0.531 0.084 0.181 2.16517 2.517 0.923 -0.448 0.081 0.006 0.07818 2.533 0.929 -0.367 0.079 0.026 0.32919 2.600 0.956 -0.287 0.078 0.032 0.40620 2.683 0.987 -0.210 0.077 0.043 0.55621 2.800 1.030 -0.133 0.076 0.012 0.15622 2.833 1.041 -0.057 0.076 0.040 0.53423 2.950 1.082 0.018 0.076 0.044 0.58324 3.083 1.126 0.094 0.076 0.068 0.89225 3.300 1.194 0.170 0.077 0.010 0.13026 3.333 1.204 0.248 0.079 0.044 0.55627 3.483 1.248 0.327 0.082 0.065 0.79728 3.717 1.313 0.408 0.085 0.094 1.10529 4.083 1.407 0.493 0.090 0.104 1.16130 4.533 1.511 0.583 0.097 0.147 1.51531 5.250 1.658 0.680 0.107 0.125 1.16932 5.950 1.783 0.787 0.123 0.008 0.06833 6.000 1.792 0.910 0.151 0.000 0.00034 6.000 1.792 1.061 0.215 0.011 0.05235 6.067 1.803 1.276 0.079 0.071 0.90536 6.517 1.874 1.355

Jumlah 4.357 1.783 16.419

Keterangan :Rank umur (ti) = waktu reparasi yang diurutkan kecil ke besarXi = ln(ti)

Rank Umur (ti) Mi ln(ti + 1) - ln(ti)(ln(ti + 1) - ln(ti)) / Mi(ln ti)

iii ZZM 1

25.05.01lnln

niZ i

4.2.8.2 Pengujian kecocokan Distribusi / Pengujian Mann's Test

Ho : Data berdistribusi WeibullHa : Data tidak berdistribusi Weibull

r = Banyaknya data (n)= 36

= 362

= 18.00

= ( 36 - 1)2

= 17.5

daerah penerimaan

=18 X 16.442

17.5 X 16.442 daerah penolakan

= 1.029

Numerator Denominator = 2 x 17.5 = 2 x 18 = 35 = 36

F(0.05,N,D) 1.748 FINV(0.05, Numerator, Denumerator)

Jika M < F crit maka terima Ho dan tolak HaJika M > F crit maka tolak Ho dan terima HaKesimpulan :Karena M < F yaitu 1,029 < 1.748 , terima Ho dan tolak Ha.Dari kesimpulan diatas, maka dapat diketahui bahwa data waktu reparasi dari komponen mesin tersebut adalah berdistribusi Weibull.Maka dari itu, dapat dilakukan perhitungan plot Weibull.

2k2 2k1

21rk

21

2

rk

1

1

1

12

1

1

11

lnln

lnln

k

i i

ii

r

ki i

ii

Mttk

Mttk

M

5%

1.029 1.748

=

18 ∑i=19

35 lnti+1−lntiMi

17.5∑i=1

18 lnti+1−lntiMi

4.2.8.3 Tabel Perhitungan Plot Weibull Waktu Reparasi Komponen Power head

i ti Xi = ln ti F ( ti ) 1 / {1 - F (ti)} ln ( E ) Yi = ln ( F )A B C D E F G1 1.000 0.000 0.019 1.020 0.019 -3.9422 1.000 0.000 0.047 1.049 0.048 -3.0403 1.133 0.125 0.074 1.080 0.077 -2.5634 1.233 0.209 0.102 1.113 0.107 -2.2335 1.250 0.223 0.129 1.148 0.138 -1.9796 1.383 0.324 0.157 1.186 0.170 -1.7707 1.683 0.521 0.184 1.226 0.203 -1.5928 1.750 0.560 0.212 1.268 0.238 -1.4379 1.783 0.578 0.239 1.314 0.273 -1.29810 1.867 0.624 0.266 1.363 0.310 -1.17111 1.883 0.633 0.294 1.416 0.348 -1.05512 1.917 0.651 0.321 1.474 0.388 -0.94713 1.933 0.659 0.349 1.536 0.429 -0.84614 2.033 0.710 0.376 1.604 0.472 -0.75015 2.100 0.742 0.404 1.677 0.517 -0.65916 2.100 0.742 0.431 1.758 0.564 -0.57217 2.517 0.923 0.459 1.848 0.614 -0.48818 2.533 0.929 0.486 1.947 0.666 -0.40619 2.600 0.956 0.514 2.056 0.721 -0.32720 2.683 0.987 0.541 2.180 0.779 -0.25021 2.800 1.030 0.569 2.318 0.841 -0.17322 2.833 1.041 0.596 2.476 0.907 -0.09823 2.950 1.082 0.624 2.657 0.977 -0.02324 3.083 1.126 0.651 2.866 1.053 0.05225 3.300 1.194 0.679 3.111 1.135 0.12726 3.333 1.204 0.706 3.402 1.224 0.20227 3.483 1.248 0.734 3.753 1.322 0.27928 3.717 1.313 0.761 4.184 1.431 0.35929 4.083 1.407 0.788 4.727 1.553 0.44030 4.533 1.511 0.816 5.433 1.692 0.52631 5.250 1.658 0.843 6.386 1.854 0.61732 5.950 1.783 0.871 7.745 2.047 0.71633 6.000 1.792 0.898 9.838 2.286 0.82734 6.000 1.792 0.926 13.481 2.601 0.95635 6.067 1.803 0.953 21.412 3.064 1.12036 6.517 1.874 0.981 52.000 3.951 1.374

Gambar 5.6 Plot Weibull Waktu Reparasi Table Adjusting

0 1 2

-5

-4

-3

-2

-1

0

1

2 Plot Weibull Waktu Reparasi (Xi vs Yi)

Xi

Yi

4,03,0

nitiF

4.2.8.4. Tabel Parameter Weibull dari Waktu Reparasi komponen Power Head

i Xi Yi XiYi1 0.000 -3.942 0.000 0.0002 0.000 -3.040 0.000 0.0003 0.125 -2.563 -0.321 0.0164 0.209 -2.233 -0.468 0.0445 0.223 -1.979 -0.442 0.0506 0.324 -1.770 -0.574 0.1057 0.521 -1.592 -0.829 0.2718 0.560 -1.437 -0.804 0.3139 0.578 -1.298 -0.751 0.33410 0.624 -1.171 -0.731 0.39011 0.633 -1.055 -0.668 0.40112 0.651 -0.947 -0.617 0.42313 0.659 -0.846 -0.558 0.43514 0.710 -0.750 -0.533 0.50415 0.742 -0.659 -0.489 0.55016 0.742 -0.572 -0.424 0.55017 0.923 -0.488 -0.450 0.85218 0.929 -0.406 -0.378 0.86419 0.956 -0.327 -0.313 0.91320 0.987 -0.250 -0.246 0.97421 1.030 -0.173 -0.178 1.06022 1.041 -0.098 -0.102 1.08523 1.082 -0.023 -0.025 1.17024 1.126 0.052 0.058 1.26825 1.194 0.127 0.151 1.42526 1.204 0.202 0.244 1.45027 1.248 0.279 0.349 1.55728 1.313 0.359 0.471 1.72429 1.407 0.440 0.620 1.97930 1.511 0.526 0.795 2.28431 1.658 0.617 1.024 2.75032 1.783 0.716 1.278 3.18033 1.792 0.827 1.482 3.21034 1.792 0.956 1.713 3.21035 1.803 1.120 2.019 3.25036 1.874 1.374 2.575 3.513Σ 24.910 -25.018 -6.188 25.741

=36(-6.118) - (24.910)(-25.018) = exp

= 1.308 = 3.398

MTTR = θ

== 3.398

= -1.600= 5.997 jam

b

= 1.308

Xi2

36(25.741) - (24.910)2

β =

22

ii

iiii

XXnYXYXn

b

nX

bnY

a ii

θ=exp(−ab )

(−25.018)36 −2.083 (24.910)

36

[1+1β ]

(−(−1.600 )

1.308 )

[1+1

1.038 ]

4.2.8.5 Perhitungan fungsi - fungsi distribusi Weibull untuk komponen Power Head, sebagai berikut :

Fungsi distribusi kumulatif waktu reparasi : Fungsi keandalan waktu Reparasi :

Fungsi kepadatan kemungkinan waktu reparasi : Fungsi laju kerusakan :

4.2.3.6 Tabel Hasil Perhitungan Fungsi Distribusi Kumulatif, Fungsi Kepadatan Kemungkinan Fungsi Keandalan, dan Fungsi Laju Kerusakan Waktu Reparasi Power Head.

t R ( t ) F ( t ) f ( t ) h ( t )1.000 0.817 0.183 0.216 0.2641.000 0.817 0.183 0.216 0.2641.133 0.788 0.212 0.216 0.2741.233 0.767 0.233 0.216 0.2821.250 0.763 0.237 0.216 0.2831.383 0.735 0.265 0.214 0.2921.683 0.671 0.329 0.208 0.3101.750 0.657 0.343 0.206 0.3141.783 0.650 0.350 0.205 0.3161.867 0.633 0.367 0.203 0.3201.883 0.630 0.370 0.202 0.3211.917 0.623 0.377 0.201 0.3231.933 0.620 0.380 0.201 0.3242.033 0.600 0.400 0.197 0.3292.100 0.587 0.413 0.195 0.3322.100 0.587 0.413 0.195 0.3322.517 0.509 0.491 0.179 0.3512.533 0.506 0.494 0.178 0.3522.600 0.494 0.506 0.175 0.3542.683 0.480 0.520 0.172 0.3582.800 0.460 0.540 0.167 0.3632.833 0.455 0.545 0.165 0.3642.950 0.436 0.564 0.160 0.3683.083 0.415 0.585 0.155 0.3733.300 0.382 0.618 0.146 0.3813.333 0.377 0.623 0.144 0.3833.483 0.356 0.644 0.138 0.3883.717 0.325 0.675 0.129 0.3964.083 0.280 0.720 0.114 0.4074.533 0.233 0.767 0.098 0.4215.250 0.171 0.829 0.075 0.4405.950 0.125 0.875 0.057 0.4576.000 0.122 0.878 0.056 0.4586.000 0.122 0.878 0.056 0.4586.067 0.118 0.882 0.054 0.4606.517 0.096 0.904 0.045 0.470

f (t)=βθ (tθ)

β−1exp[−(tθ)

β ]

F (t )=1−exp [−(tθ)β ] R (t)=exp[−(tθ )

β]

h (t )=βθ (tθ )

β−1

=exp[−( t5.997 )

1.308 ]=1−exp [−( t5.997 )

1.308]

=1.3085.997 ( t

5.997 )1.308−1

=1.3085.997 ( t

5.997 )1.308−1

exp [−( t5.997 )

1.308]

Berdasarkan perhitungan pada tabel diatas, maka dapat ditentukan kurva dari beberapa fungsi yang dapat dilihat pada gambar berikut :

Gmabar 5.2 Kurva fungsi keandalan waktu reparasi

Gmabar 5.3 Kurva fungsi distribusi kumulatif waktu reparasi

Gmabar 5.4 Kurva fungsi kepadatan kemungkinan waktu reparasi

Gmabar 5.5 Kurva fungsi laju kerusakan

0 1 2 3 4 5 6 70.000.200.400.600.801.00

Kurva Fungsi Distribusi Kumulatif Waktu Reparasi

t (jam)

F(t)

0 1 2 3 4 5 6 70.0000.0500.1000.1500.2000.250

Kurva Fungsi Kepadatan Kemungkinan Waktu Reparasi

t (jam)

f(t)

0 1 2 3 4 5 6 70.0000.2000.4000.6000.8001.000

Kurva Fungsi Keandalan Waktu Reparasi

t (jam)

R(t)

0 1 2 3 4 5 6 70.0000.1000.2000.3000.4000.500

Kurva Fungsi Laju Kerusakan

t (jam)

h(t)